Canonical combined lesson MATH30B-L081 · week 17 day 1 · CURRICULUM_BASELINE

MATH30B-L081 - Cumulative: functions through explog; logic through explog; measure through linear

• Delivery id: MATH30B (combined classroom; not a fourth credential)
• Official courses: Mathematics 30-1 (MAT3791), 30-2 (MAT3792), 30-3 (MAT3793)
• Lesson ID: MATH30B-L081
• Calendar: Week 17 Day 1 of 18 weeks × 5 days (lesson 81 of 90)
• Object type: canonical combined-classroom lesson
• Braid class: C
• Labels: ALL STRANDS launch → 30-1 REQUIRED / 30-2 REQUIRED / 30-3 REQUIRED workshops → CROSS-STRAND EXPOSURE ≠ mastery
• Source: Alberta Mathematics 10-12 Program of Studies, https://open.alberta.ca/publications/mathematics-grades-10-12
• Official outcome IDs today: MATH30-1-TRIGONOM-01-007, MATH30-1-TRIGONOM-02-008, MATH30-1-TRIGONOM-06-012, MATH30-1-TRIGONOM-07-013, MATH30-1-TRIGONOM-08-014, MATH30-1-TRIGONOM-09-015, MATH30-1-TRIGONOM-10-016, MATH30-2-X-01-001, MATH30-2-LOGICALR-02-002, MATH30-2-LOGICALR-04-012, MATH30-2-RELATION-05-013, MATH30-2-RELATION-06-014, MATH30-3-X-01-001, MATH30-3-ALGEBRA-01-008

Labels (post on the board)

1. ALL STRANDS - shared launch only.
2. 30-1 REQUIRED - MAT3791 tray; mastery evidence for 30-1 SOs listed below.
3. 30-2 REQUIRED - MAT3792 tray; mastery evidence for 30-2 SOs listed below.
4. 30-3 REQUIRED - MAT3793 tray; mastery evidence for 30-3 SOs listed below.
5. CROSS-STRAND EXPOSURE ≠ mastery - hearing another tray is logged as EXPOSURE, never as an SO tick, never as a silent enrolment change.

ALL STRANDS launch (~10-14 min)

Spiral original items. Coverage is still home-strand REQUIRED.

Clock ~75 min unless the school uses 60; cut the workshop block first, never the strand exit ticket. Class C parallel workshops are the default when one strand is on exclusive work.

Official outcomes (REQUIRED on home strand)

Strand	Official ID	Role today
30-1	MATH30-1-TRIGONOM-01-007	REQUIRED - Demonstrate an understanding of operations on, and compositions of, functions
30-1	MATH30-1-TRIGONOM-02-008	REQUIRED - Demonstrate an understanding of the effects of horizontal and vertical translations on the graphs of functions and their related equations
30-1	MATH30-1-TRIGONOM-06-012	REQUIRED - Demonstrate an understanding of inverses of relations
30-1	MATH30-1-TRIGONOM-07-013	REQUIRED - Demonstrate an understanding of logarithms
30-1	MATH30-1-TRIGONOM-08-014	REQUIRED - Demonstrate an understanding of the product, quotient and power laws of logarithms
30-1	MATH30-1-TRIGONOM-09-015	REQUIRED - Graph and analyze exponential and logarithmic functions
30-1	MATH30-1-TRIGONOM-10-016	REQUIRED - Solve problems that involve exponential and logarithmic equations
30-2	MATH30-2-X-01-001	REQUIRED - Analyze puzzles and games that involve numerical and logical reasoning, using problem-solving strategies
30-2	MATH30-2-LOGICALR-02-002	REQUIRED - Solve problems that involve the application of set theory
30-2	MATH30-2-LOGICALR-04-012	REQUIRED - Demonstrate an understanding of logarithms and the laws of logarithms
30-2	MATH30-2-RELATION-05-013	REQUIRED - Solve problems that involve exponential equations
30-2	MATH30-2-RELATION-06-014	REQUIRED - Represent data, using exponential and logarithmic functions, to solve problems
30-3	MATH30-3-X-01-001	REQUIRED - Demonstrate an understanding of the limitations of measuring instruments, including: • precision • accuracy • uncertainty • tolerance and solve problems
30-3	MATH30-3-ALGEBRA-01-008	REQUIRED - Demonstrate an understanding of linear relations by: • recognizing patterns and trends • graphing • creating tables of values • writing equations • interpolating and extrapolating

30-1 workshop - 30-1 REQUIRED

Clock: ~22-28 min after launch (cut workshop before cutting the strand exit ticket). Learners on this tray stay on 30-1.

MATH30-1-TRIGONOM-01-007

Official text: Demonstrate an understanding of operations on, and compositions of, functions

Worked example (unique to this hour, this strand, this SO): f(x)=6x+4, g(x)=x²−2. Compute (f∘g)(7) and (g∘f)(x). State the domain of (f∘g) if instead g(x)=√(x−2).

Level	Prompt (inside the home strand)
FOUNDATION	Numeric f(3).
CORE	(f∘g)(x) algebraic.
PROFICIENT	Domain of a composition.
ADVANCED	(f∘f⁻¹)(x)=x justification.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Mapping diagrams for f and g; composition arrows.

MATH30-1-TRIGONOM-02-008

Official text: Demonstrate an understanding of the effects of horizontal and vertical translations on the graphs of functions and their related equations

Worked example (unique to this hour, this strand, this SO): Parent f(x)=x². Write the equation of the image after shift 4 right and 6 up: y=(x−4)²+6. The point (0,0) maps to (4,6). Match a graphed image to y=f(x+2)−7.

Level	Prompt (inside the home strand)
FOUNDATION	Shift a table of values up 2.
CORE	Write y=f(x−h)+k.
PROFICIENT	Equation from a graphed image.
ADVANCED	Composition with a translation.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Parent-to-image graphs for y=f(x−h)+k.

MATH30-1-TRIGONOM-06-012

Official text: Demonstrate an understanding of inverses of relations

Worked example (unique to this hour, this strand, this SO): Find the inverse of f(x)=6x−4. Restrict if needed so the inverse is a function. Show (f∘f⁻¹)(x)=x on that domain. Numeric undo: f(7) then invert.

Level	Prompt (inside the home strand)
FOUNDATION	Numeric undo.
CORE	Swap coordinates on a table.
PROFICIENT	Algebraic inverse with domain.
ADVANCED	Prove composition identity.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Inverse visual: points swapped; y=x mirror.

MATH30-1-TRIGONOM-07-013

Official text: Demonstrate an understanding of logarithms

Worked example (unique to this hour, this strand, this SO): Rewrite 6^7=279936 in log form. Evaluate log_6(36) exactly. Explain log_61=0 and why log_6(−4) is not real.

Level	Prompt (inside the home strand)
FOUNDATION	log_10 1000.
CORE	Convert b^x=a to log form.
PROFICIENT	Exact log of a power of the base.
ADVANCED	Change-of-base preview.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. VIS-M30-EXPLOG: y=b^x and y=log_b x as inverse graphs.

MATH30-1-TRIGONOM-08-014

Official text: Demonstrate an understanding of the product, quotient and power laws of logarithms

Worked example (unique to this hour, this strand, this SO): Expand log_6(x^4 y) for x,y>0: 4 log_6 x + log_6 y. Condense log_6 7 − log_6 2 + 4 log_6 6. Reject the illegal step log u + log v = log(u+v) with a counter-example using 6 and 4.

Level	Prompt (inside the home strand)
FOUNDATION	One law: log(xy).
CORE	Expand or condense mixed laws.
PROFICIENT	Justify each step.
ADVANCED	Counter-example to log(u+v).

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Log-law cards (product, quotient, power) posted after retrieval.

MATH30-1-TRIGONOM-09-015

Official text: Graph and analyze exponential and logarithmic functions

Worked example (unique to this hour, this strand, this SO): Graph y=6^x and y=log_6 x. State intercepts, asymptotes, and domain/range. Compare to y=6^{x−2}+4.

Level	Prompt (inside the home strand)
FOUNDATION	Intercept of y=2^x.
CORE	Asymptote and domain of log.
PROFICIENT	Describe a transformed explog graph.
ADVANCED	Compare two bases on one axes.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Exp and log graphs with intercepts, asymptotes, and end behaviour.

MATH30-1-TRIGONOM-10-016

Official text: Solve problems that involve exponential and logarithmic equations

Worked example (unique to this hour, this strand, this SO): Solve 6^x = 7 exactly (x=log_6 7) then a decimal check. Solve log_6(x−2)+log_6 x = log_6 7 with domain x>2 (and x>0). Reject extraneous roots.

Level	Prompt (inside the home strand)
FOUNDATION	Solve 2^x=8.
CORE	Exact then tech check.
PROFICIENT	Log equation with domain.
ADVANCED	Extraneous root rejected.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Equation-graph link: intersection of y=b^x and y=k.

Independent practice: a new instance of today’s SO(s) with different numbers than the worked example. Two sentences on reasonableness.

Wrong-answer repair (do not praise):

• 30-1 SO 007: Computing (f∘g) as f(x)·g(x), or ignoring domain of the inner function. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-1 SO 008: Writing y=f(x−h) as a shift left when h>0, or sliding a 30-3 shape and calling it SO 008. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-1 SO 012: Swapping a and b in y=ax+b incorrectly, or claiming every inverse is a function. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-1 SO 013: Writing log_b a = b^a, or logging a negative as if it were real. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-1 SO 014: log u + log v = log(u+v), or bringing an exponent across a sum inside a log. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-1 SO 015: Drawing y=log_b x with a y-intercept of 1, or an asymptote on the y-axis forgotten. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-1 SO 016: Exponentiating only one side, or keeping an extraneous root from a log domain. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.

30-2 workshop - 30-2 REQUIRED

Clock: ~22-28 min after launch (cut workshop before cutting the strand exit ticket). Learners on this tray stay on 30-2.

MATH30-2-X-01-001

Official text: Analyze puzzles and games that involve numerical and logical reasoning, using problem-solving strategies

Worked example (unique to this hour, this strand, this SO): KenKen-style or “exactly one of these three statements is true” puzzle using numbers 6,4,7. Name the strategy (eliminate / work backward / guess-check) and transfer it to a second mini-puzzle.

Level	Prompt (inside the home strand)
FOUNDATION	Attempt the puzzle with hints.
CORE	Solve and name a strategy.
PROFICIENT	Transfer to a second puzzle.
ADVANCED	Write a false-friend statement.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Puzzle card with a named strategy box (guess-check, eliminate, work backward).

MATH30-2-LOGICALR-02-002

Official text: Solve problems that involve the application of set theory

Worked example (unique to this hour, this strand, this SO): In a class of 26, 13 like chlorine tablets, 13 like filters, 5 like both. Draw the Venn. Find only-tablets, only-filters, neither, and n(A∪B).

Level	Prompt (inside the home strand)
FOUNDATION	Place two numbers in a Venn.
CORE	Compute union with overlap.
PROFICIENT	Three-set or complement.
ADVANCED	Word problem with “neither”.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Venn diagram VIS-M30B-SET (two or three sets) after retrieval.

MATH30-2-LOGICALR-04-012

Official text: Demonstrate an understanding of logarithms and the laws of logarithms

Worked example (unique to this hour, this strand, this SO): Users grow from 60 at annual factor 1.07. Write a log to find years to reach 180. Apply one product or power law in the setup, then a technology check. Not 30-1 exact-only demand.

Level	Prompt (inside the home strand)
FOUNDATION	Meaning of log in a growth sentence.
CORE	One law in a story.
PROFICIENT	Tech check after setup.
ADVANCED	Reasonableness limits.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. VIS-M30-EXPLOG in a growth story (not 30-1 exact-only demand).

MATH30-2-RELATION-05-013

Official text: Solve problems that involve exponential equations

Worked example (unique to this hour, this strand, this SO): Solve 1.07^t = 3 using logs or tech after a table guess. State what the solution means for the water-enterprise users and one model limit.

Level	Prompt (inside the home strand)
FOUNDATION	Guess-check table for a^t=k.
CORE	Log or tech solve.
PROFICIENT	Model limits.
ADVANCED	Compare two growth models.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Table-to-equation growth model.

MATH30-2-RELATION-06-014

Official text: Represent data, using exponential and logarithmic functions, to solve problems

Worked example (unique to this hour, this strand, this SO): Given points (0,16), (1,17), (2,18), choose exponential vs linear and write a model in words plus an equation. Residual: one point off by 6.

Level	Prompt (inside the home strand)
FOUNDATION	Table to graph.
CORE	Choose exp vs linear.
PROFICIENT	Fit language.
ADVANCED	Residual talk.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Scatter + exponential/log model VIS-M30B-DATA.

Independent practice: a new instance of today’s SO(s) with different numbers than the worked example. Two sentences on reasonableness.

Wrong-answer repair (do not praise):

• 30-2 SO 001: Guessing without naming a strategy, or claiming a unique solution when two remain. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-2 SO 002: Adding n(A)+n(B) without subtracting the intersection. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-2 SO 012: Applying 30-1 exact-only demands as if they were this SO, or illegal log sums. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-2 SO 013: Reporting a negative time without checking the model. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-2 SO 014: Forcing a linear model on clearly exponential data. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.

30-3 workshop - 30-3 REQUIRED

Clock: ~22-28 min after launch (cut workshop before cutting the strand exit ticket). Learners on this tray stay on 30-3.

MATH30-3-X-01-001

Official text: Demonstrate an understanding of the limitations of measuring instruments, including: • precision • accuracy • uncertainty • tolerance and solve problems

Worked example (unique to this hour, this strand, this SO): A cylinder scale is marked every 2 mL. A reading looks like 121 mL. State precision, a reasonable uncertainty interval, and whether a ±6 mL tolerance is met. Accuracy still needs a true value - do not call a precise reading accurate by default.

Level	Prompt (inside the home strand)
FOUNDATION	Read to nearest mark; copy precision vs accuracy.
CORE	Uncertainty interval.
PROFICIENT	Tolerance met/not.
ADVANCED	Choose an instrument for the job.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Ruler/scale photos VIS-M30B-MEAS (precision vs accuracy).

MATH30-3-ALGEBRA-01-008

Official text: Demonstrate an understanding of linear relations by: • recognizing patterns and trends • graphing • creating tables of values • writing equations • interpolating and extrapolating • solving problems

Worked example (unique to this hour, this strand, this SO): Table: hours 0, 1, 2, 3 vs litres treated 0, 18, 36, 54. Graph, write litres = (rate)(hours), interpolate at 1.5 h, extrapolate to 5 h with a caution.

Level	Prompt (inside the home strand)
FOUNDATION	Complete a table.
CORE	Graph + equation.
PROFICIENT	Interpolate.
ADVANCED	Extrapolate with caution.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. VIS-M30B-LINEAR: table, graph, equation together.

Independent practice: a new instance of today’s SO(s) with different numbers than the worked example. Two sentences on reasonableness.

Wrong-answer repair (do not praise):

• 30-3 SO 001: Calling a precise instrument accurate, or writing uncertainty as a single point. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-3 SO 008: Extrapolating far beyond the table with no caution. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.

CROSS-STRAND EXPOSURE ≠ mastery

• CROSS-STRAND EXPOSURE ≠ mastery. Log D items. Do not tick another strand’s SO.
• AI Tutor must not treat an exposure card as proficiency.

Project or clean math

Project overlay today: none. Use a clean math prompt on the home-strand tray. Do not force Sustainable Community Water & Hygiene onto work that is not genuinely that mathematics.

AI Tutor

• Load the authorized home strand only: MAT3791 (Mathematics 30-1) or MAT3792 (Mathematics 30-2) or MAT3793 (Mathematics 30-3) from the authorized profile.
• Never silent-switch a struggling 30-1 learner into 30-2/30-3 banks (or the reverse) to “make it easier.”
• Serve today’s home-strand SOs. Exposure cards are read-only.
• Never dump diploma keys or released exam wording. Original items only.
• Wrong answers: name the error and repair; do not praise.

Human-tutor handoff

Call a human tutor when: the learner cannot complete CORE after two documented repairs; an identity proof (30-1 006) is stuck after the identity map; a 30-2 017 source is unsafe or empty; a 30-3 vehicle/business number is being faked to match a hoped-for answer; distress, disclosure, or a request to change official enrolment. Enrolment changes are an office/PASI process, not a tutor action.

Diagram / whiteboard

Approved starter math30-quadratic-shift. Strand workshops may add axes/tables. Never praise a translated parabola as a circle.

Strand exit ticket (~8-12 min)

Collect only the home-strand row. Exposure ≠ mastery. Lesson MATH30B-L081.

Home strand	Primary SO	Exit ticket (unique to this lesson)
30-1	MATH30-1-TRIGONOM-01-007	CORE exit: f(x)=6x+4, g(x)=x²−2. Compute (f∘g)(7) and (g∘f)(x). State the domain of (f∘g) if instead g(x)=√(x−2). FOUNDATION alternate: Numeric f(3). Do not submit another strand’s ticket as 30-1 mastery.
30-2	MATH30-2-X-01-001	CORE exit: KenKen-style or “exactly one of these three statements is true” puzzle using numbers 6,4,7. Name the strategy (eliminate / work backward / guess-check) and transfer it to a second mini-puzzle. FOUNDATION alternate: Attempt the puzzle with hints. Do not submit another strand’s ticket as 30-2 mastery.
30-3	MATH30-3-X-01-001	CORE exit: A cylinder scale is marked every 2 mL. A reading looks like 121 mL. State precision, a reasonable uncertainty interval, and whether a ±6 mL tolerance is met. Accuracy still needs a true value - do not call a precise r… FOUNDATION alternate: Read to nearest mark; copy precision vs accuracy. Do not submit another strand’s ticket as 30-3 mastery.

Provenance

Official IDs/text: _official_math_calm_outcomes.json. Pacing: MATH30_COMBINED_CLASSROOM_PACING.md. Crosswalk: MATH30_1_30_2_30_3_OUTCOME_CROSSWALK.csv. Generated by oeom/core/training/rapid3/write_math30b_lessons.py.